Republican US presidential candidate Donald Trump makes a face as he and his wife Melania and members of their family leave the stage at his caucus night rally in Des Moines, Iowa. Now Trump has accused Ted Cruz of fraud in the caucus. Photo: Reuters/Scott Morgan

In attacks posted on his official Twitter account yesterday, Mr Trump said "either a new election should take place or Cruz results nullified" in Monday's Iowa contest. The billionaire businessman was placed second behind the conservative Texas senator.

Thank you @billoreilly & @KarlRove. Ted Cruz should be immediately disqualified in Iowa, with each candidate moving up one notch.

A previous Trump tweet accused the Cruz campaign of telling Iowa voters that Ben Carson was quitting the race so he could steal Mr Carson's votes.

Meanwhile, Rand Paul who has bowed out of the race said he will now turn his full attention to his Senate re-election campaign in Kentucky.

Florida Sen. Marco Rubio, who was placed third among the Republicans in Iowa, said he will try to persuade some of Rand Paul's supporters to redirect their support to him, despite the stark differences the two have on foreign policy.

Both men were elected to the Senate during the rise of the conservative tea party in 2010. Rubio is trying to be the Republican establishment's preferred alternative to Trump or Cruz.

Meanwhile, an anonymous US politician has put forward Republican presidential candidate Donald Trump for the Nobel Peace Prize in one of the most unlikely nominations since that of Soviet strongman Josef Stalin in 1947.

The nominator, likely to be a Republican senator or congressman - both of whom are eligible - submitted the nomination only days before the deadline of February 1.

Kristian Berg Harpviken, director of Oslo's Peace Research Institute, which publishes an annual prediction of the likely prize-winner, confirmed that he had been sent a copy of the Trump nomination letter last week.

"I have committed not to reveal the identity of the nominator, but what I can say is that the nominator has shared a copy of his nomination letter directly with me, that the nominator has a position which gives him the right to nominate, and that I consider it valid."

Mr Trump has seen support among Republican voters soar to 40pc this year as he outrages liberals with his calls to ban Muslims from entering the US, describes Latino Americans as "rapists", and pledges to "beat the s---" out of Isil with indiscriminate carpet bombing.

"When you get these terrorists, you have to take out their families," Mr Trump said in December, when asked about his approach to tackling Isil in Syria and Iraq.

Mr Harpviken described a Trump prize as "entirely unlikely", arguing that the reason put forward, which appeared to be "about the necessity of confrontation rather than anything else" would not convince the five-member committee.

His shortlist of the 11 most likely winners was this year headed by US surveillance whistleblower Edward Snowden.

Mr Harpviken argued that surveillance oversight reforms in the US, and a vote in the European Parliament calling on member states to "drop any criminal charges" against Mr Snowden made his chances of winning the award greater this year than in either 2014 or 2015, when he was also nominated.

Mr Harpviken's second tip is the duo of Ernest Moniz, the US energy secretary, and Ali Akbar Salehi, the head of the Atomic Energy Organisation of Iran for their part in the Iran nuclear deal.

The third most likely winner in his opinion was the duo of Timoleón Jiménez, head of Colombia's FARC guerrillas, and Colombian president Juan Manuel Santos, for their part in peace talks to end the long-running Columbian civil war.